Hydroelastic stability of a rectangular plate interacting with a layer of ideal flowing fluid
| Autor: | Valery P. Matveenko, S. V. Lekomtsev, S. A. Bochkarev |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Fluid Flow and Transfer Processes
Physics Mechanical Engineering General Physics and Astronomy Perfect fluid 02 engineering and technology Mechanics 01 natural sciences Instability Finite element method 010305 fluids & plasmas 020303 mechanical engineering & transports Classical mechanics 0203 mechanical engineering Dynamic problem Variational principle 0103 physical sciences Fictitious force Velocity potential Boundary value problem |
| Zdroj: | Fluid Dynamics. 51:821-833 |
| ISSN: | 1573-8507 0015-4628 |
| DOI: | 10.1134/s0015462816060132 |
| Popis: | The three-dimensional formulation of the problem on the natural vibrations and stability of an elastic plate which interacts with a quiescent or flowing fluid is represented and a finite element algorithm of its numerical implementation is proposed. The governing equations, which describe vortex-free ideal fluid dynamics in the case of small perturbations, are written in terms of the perturbation velocity potential and transformed using the Bubnov–Galerkin method. The plate strains are determined on the basis of the Timoshenko theory. The variational principle of virtual displacements which takes into account the work done by inertial forces and the hydrodynamic pressure is used for the mathematical formulation of the dynamic problem of elastic structure. The solution of the problem is reduced to calculations and an analysis of complex eigenvalues of a coupled system of two equations. The effect of the fluid layer height on the eigenfrequencies and the critical velocities of the loss of stability is estimated numerically. It is shown that there exist different types of instability determined by combinations of the kinematic boundary conditions prescribed at the plate edges. |
| Databáze: | OpenAIRE |
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